A behavioural view of play in mechanical networks

This paper shows that the treatment of play as an input-output operator in mechanical networks leads to solutions which are unsatisfactory from a physical point of view. This contrasts with a simple behavioural definition of ideal play. With this definition, play cannot be treated in isolation as an input-output relation. As a result, methods of non-linear feedback systems are not readily applicable to establish well-posedness of solutions of mechanical networks incorporating this play element. By means of simple network examples this paper explores the issues involved in establishing well-posedness of mechanical networks incorporating springs, dampers, masses and inerters together with the behavioural model of ideal play. Connections with the approach of Nordin, Galic and Gutman are highlighted.